correlation and regression

Question 1

what may be related to each other? - give an example

Answer 1

• two datasets may be related
  e.g., height, weight

Question 2

when can you see the relationship of the datasets?

Answer 2

• when you look at them on a graph

Question 3

what were the first statistics invented for?

Answer 3

• for analysing co- relationships

Question 4

when is there probably a mistake in data?

Answer 4

• if your data shows a perfect straight line
• if there’s more than one datapoints a long way away from all the others

Question 5

when might data be worth checking for mistakes?

Answer 5

• if there’s no relationship at all between things you really expect to be related

Question 6

what is the definition of correlation?

Answer 6

• finds the best fit line by minimising the difference between the data and line

Question 7

what does a correlation report about a relationship?

Answer 7

• strength and direction of a relationship

Question 8

what is a residual?

Answer 8

• difference between an observed value and a predicted value in regression analysis

Question 9

what is a zero correlation?

Answer 9

• no relationship between the variables
• cluster of data points

Question 10

what is a positive correlation?

Answer 10

• relationship between two variables that tend to move in the same direction

Question 11

what is a negative correlation

Answer 11

• two individual variables generally move in opposite directions

Question 12

what would you do to get the line of best fit?

Answer 12

• could try adjust the line manually but wouldn’t be the best fit
• need to use maths instead

Question 13

what equation allows you to work out the line of best fit?

Answer 13

r = Sxy/ Sx.Sy

Question 14

what does Sxy stand for?

Answer 14

• how much x and y change together

Question 15

what is Sx. Sy?

Answer 15

• how much x and y change separately

Question 16

what is the equation to work out r?

Answer 16

n/i = 1 (xi-x)(yi-y) / square root of n/i= 1 (xi-x)^2 square root of n/i= 1 (yi- y) ^2

Question 17

what two aspects does a R value tell you?

Answer 17

• direction
• strength

Question 18

what value is r when the correlation is positive?

Answer 18

• if r is above 0
  1 > r > 0

Question 19

what value is r when the correlation is negative?

Answer 19

• r is below zero
  -1 < r < 0

Question 20

what is the value of r when the correlation is strong?

Answer 20

• if r is close to one
  r +/- 1

Question 21

what is the r value when the correlation is weak?

Answer 21

• r is close to zero
  r- 0

Question 22

when are r values especially useful?

Answer 22

• useful for values in the middle e.g., - 0.4 to 0.4

Question 23

what does the r-squared value tell you?

Answer 23

• how much of the variance is explained by your correlation

Question 24

what is the r- squared value when correlation explains a lot of variance?

Answer 24

• if r2 is close to one
  r2-1

Question 25

what is the r- squared value when correlation explains only a little variance?

Answer 25

- if r2 is close to zero r2- 0

Question 26

what other name is r-squared given?

Answer 26

- coefficient of determination

Question 27

what is 1-r2?

Answer 27

- amount of variance not explained - random noise

Question 28

what is regression?

Answer 28

- gives your the strengths, directions and equations of relationships

Question 29

what is the regression equation?

Answer 29

y = mx + c

Question 30

what is m in the equation?

Answer 30

- slope

Question 31

what is c in the equation?

Answer 31

- intercept

Question 32

what happens when x= 0 ?

Answer 32

y= intercept

Question 33

what happens to y-axis when x increases by 1?

Answer 33

- y increases by the slope

Question 34

what do both correlation and regression involve?

Answer 34

- both involve linear relationships between one or more input (predictor) variables and a single output (outcome) variable

Question 35

what data can both correlation and regression deal with?

Answer 35

- categorical, ordinal, and non- linear predictors

Question 36

what relationship does correlation describe?

Answer 36

- single relationship

Question 37

what relationship does regression describe?

Answer 37

- multiple relationships

Question 38

what is the difference between X and Y in correlation compared to regression?

Answer 38

- in correlation, X and Y are inter- changeable whereas X and Y are not inter- changeable in regression

Question 39

do correlation and regression allow prediction?

Answer 39

- correlation doesn't allow prediction - regression allows prediction

Question 40

what symbols are used for correlations?

Answer 40

- R and r2

Question 41

what symbols are used for regression?

Answer 41

- R - R2 - F - t - SE - B1-n

Question 42

what does jamovi allow us to explore? what do you use?

Answer 42

- multiple relationships in one go - use a correlation matrix

Question 43

what does correlation matrix include? what do we calculate?

Answer 43

- includes all information we need but we must calculate df ourselves

Question 44

how do you calculate df?

Answer 44

df = n - 2

Question 45

how do you calculate correlations?

Answer 45

r([df])= [Pearson's r], p = [p-value]

Question 46

what is overall regression?

Answer 46

- r2= [(r2) value]

Question 47

what is the model fit of regression?

Answer 47

F ([df1], [df2]) = [F-value], p= [p-value]

Question 48

what is multiple linear regression?

Answer 48

- single outcome variable (y) but multiple predictor variables (x1, x2)

Question 49

what do you find in multiple linear regression?

Answer 49

- find the best- fitting surface

Question 50

where are residuals in multiple linear regression?

Answer 50

- residuals are distance from the surface

Question 51

what can the predictors be in multiple linear regression?

Answer 51

- predictors can be almost anything: continuous, ordinal, discrete normally- distributed or not linear or non- linear

Question 52

what is multiple linear regression said to be?

Answer 52

- flexible e.g., ChatGPT, fMRI, COVID, elections

Question 53

what does each predictor result in?

Answer 53

- result in an estimate, a standard error, a t- score and a p- value

Question 54

what is the problem with correlation and regression?

Answer 54

- extrapolation

Question 55

what does non- linear relationships cause?

Answer 55

- causes problems

Question 56

what are the solutions to the problems?

Answer 56

- look at the data - check for mistakes - perhaps transform the data: quadratic, cubic, logarithmic

Question 57

does correlation equal causation?

Answer 57

- no